If “No scientists are philosophers” is true, what may be inferred about the truth or falsehood of the following propositions? That is, which can be known to be true, which can be known to be false, and which are undetermined?
1. No nonphilosophers are scientists.
2. Some nonphilosophers are not nonscientists.
3. All nonscientists are nonphilosophers.
4. No scientists are nonphilosophers.
5. No nonscientists are nonphilosophers.
6. All philosophers are scientists.
7. Some nonphilosophers are scientists.
8. All nonphilosophers are nonscientists.
9. Some scientists are not philosophers.
10. No philosophers are nonscientists.